A number of years ago I compared my oracle delphi MkV turntable fitted with an eminent technology tone arm and a vanden hull mc cartridge - running through a morrison preamp, conrad johnson amps and quad 63 speakers.
I have a pretty good ear. I've been listening to music for many decades, studied music at university and have been building instruments since 1971 and spend a lot of time listening to minute differences between instruments that many people would never notice or listen for. I can tell for instance by ear many details about a players techniques etc. So I consider my ears fairly well trained and able to hear fairly subtle detail in music performance.
I hooked up a relatively inexpensive mass market cd player and connected the 2 through an A/B comparator box.
The box used very good cabeling, gold and mercury contact switching etc. - it was a custom laboratory equipment. The box also was able to match the two inputs for volume within .2 dB.
The box allowed the listener to choose to listen to input A (record player) or B (CD player) or push the middel button which randomly would play either A or B. The listener could listen to A or B as much as they liked and when they felt they would be able to tell the difference they would then press the middle button and after listening would then guess which they were listening to. The listener would do this a number of times and the results were recorded and checked. If the listener could tell the difference reliably then the results would clearly show this. If the listener couldn't tell then the results would be close to chance or 50/50.
We had about 20 titles that we had both the CD and LP. I did the test numerous times, so did my wife and many of my audiophile friends and even some of my none audiophile friends. The results were quite astonishing. On some of the titles nearly everyone was able to tell the difference but on most of the titles no one could reliably detect the difference.
Puzzled about this I asked an audio engineer acquaintance. It's easy he said, on some CD mastering the engineer fools around enough with settings, eq or whatever that the two formats are for all intents different recordings. These would be easy to tell apart. The recordings that had been remastered properly for CD format would sound like the LP and therefore would be indistinquishable and, they were. These results seem to show that the engineering in the recording - mikes, placement, mixing, mastering etc. have more effect on the final sound than the playback technology.
I kept doing the comparison for a week, hunting down more CD titles. At the end of the week I was convinced. I sold the table, arm and cartridge
You can try this for yourself. You will have to enlist the aid of a 2nd party to do the switching for you and act as the "random" selector since that function won't be built in and volume matching may be a little tricky too. You could use a good quality passive volume control.
I'm sure you've heard it before but - very little of our hearing goes on in our ears, most of it goes on between them, and is influenced by everything else there. If the difference is really there and audible you should be able to pick it out blindfolded.
It's an educational and fun experiment. By the way the sound level matching is important many experiments have shown that listeners will choose the louder of two choices as sounding better pretty much every time.

I think much depends on the kind of setup-as I said before my new cartridge did a lot to tell the two media apart.
Of course when you compare you should always start from the same master tape- gone LP and then gone CD. And of course you should start from a good recording. For instance Beethoven on DG is just the same on LPs and CDs.
But when I listen to Keith Jarrett's Koln Concert on both CD and LP I hear a world of difference: not simply saying one is better than the other, but an awful lot of information coming out of the LP which has disappeared on CD: you can tell the micro is inside the piano, since you can hear all the long term resonances, you can hear the ringing of the little chords,...all things are not there on CD.
And with the right cartridge you can year at the beginning two people speaking-and also tell one is a man and another a woman.
Nothing on CD.
So maybe with another cartridge-phonepre or setup you could have heard all the differences (with the right recordings I have to repeat).
The moral again is: for many people the difference is not important or not there...but 10% of times there's a world of difference...and all the fun is there.

I have to chime in on this issue as I have spent considerable time doing back-and-forth comparisons of CD vs. DVD-A/SACD and Vinyl. I think that I have a very good system and good ears - also, my wife, who has no vested interest in any format and would not consider herself to be an audiophile has been a good test subject as well. I have a dedicated McIntosh MVP871 for DVD-A/SACD playback, McIntosh MCD205 CD Player, McIntosh MDA1000 D/A Converter, McIntosh C2200 Preamp, McIntosh MC402 Amplifier, Roksan Xerxes Turntable with Shelter 901 Cartridge, Martin Logan Aeon-i Speakers. While I enjoy the sound of good DVD-A/SACD and CD, I prefer the sound of Vinyl. Obviously, the quality of the Vinyl, cleanliness and condition have to be taken into account (as with the other music formats as well), but there is just something organic and right about the sound of a good Vinyl playback system. My wife as well as numerous friends would also tell you that in A/B comparisons Vinyl sounds better. I know there is a lot of discussion on the merits of Digital vs. Vinyl and on which format is superior. For me, it all comes down to which format gets me closer to live music - and in that regard, Vinyl wins out. That said, I love music and have a considerable collection of DVD-A, SACD and CD titles as well as over 1,000 albums and listen to all formats on a regular basis, but when I do serious listening, I put an album on my VPI Typhoon Record Cleaner and spin Vinyl.
Happy Listening,
Anroj

Now, there are some that have had the experience of listening to half-track, 15 ips master tapes. I have had opportunity to compare some classical choir performances (Oberlin College Choir) that I made in the early '70s with the album the school produced using my master tapes. (I used Blumlein configuration ribbon mics for the recording).

Sadly, the vinyl was poorly produced with the highs truncated by compression; none-the-less, the vinyl was decent but certainly not great. It did, however, give the opportunity to compare the two media and, to the extent that one can recall a live performance, the "real" event.

Let me state this: NOTHING REPRODUCED REALLY COMES CLOSE TO A LIVE MUSICAL PERFORMANCE!!!

In my opinion, master analogue tape are the closest we are going to get to the real thing... digital master tapes are significantly less of an approximation. These are then followed, in quality of reproduction as in my post above.

I am anxious to hear an analogue master tape transferred to Blu-Ray for audio only... if any have heard such, please let me know the source.